Continuation:

 

13.) As we have seen leads the addition of both Lunes of Alhazen to a squarable area.

 But if we subtract the area of the smaller lune from the bigger one,

 we get an area which can be transferred into a circle,

 ... as it is shown in the following graphic:

 

Lune, Hippocrates, proof

 

14.) ... and further relationships:

 

lune of Hippocrates, square, inradius, Heisss

 

15.) ... even more relationships? [here]

 

 

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